{VERSION 3 0 "DEC ALPHA UNIX" "3.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 385 "ulam:=proc(n::nonne gint)\n local PT,pt,counter,i,direction,j;\n PT[1]:=[0,0]:\n pt:=[1 ,-1];\n counter:=1;\n for i to n do\n for direction in [[0,1],[-1 ,0],[0,-1],[1,0]] do\n for j to 2*i do\n pt:=[pt[1]+direct ion[1],pt[2]+direction[2]];\n counter:=counter+1;\n PT[c ounter]:=pt\n od\n od;\n pt:=[pt[1]+1,pt[2]-1] \n od;\n [ seq(PT[i],i=1..(2*n+1)^2)]\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "ulam(3);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7S7$\"\"!F %7$\"\"\"F%7$F'F'7$F%F'7$!\"\"F'7$F+F%7$F+F+7$F%F+7$F'F+7$\"\"#F+7$F1F %7$F1F'7$F1F17$F'F17$F%F17$F+F17$!\"#F17$F9F'7$F9F%7$F9F+7$F9F97$F+F97 $F%F97$F'F97$F1F97$\"\"$F97$FCF+7$FCF%7$FCF'7$FCF17$FCFC7$F1FC7$F'FC7$ F%FC7$F+FC7$F9FC7$!\"$FC7$FOF17$FOF'7$FOF%7$FOF+7$FOF97$FOFO7$F9FO7$F+ FO7$F%FO7$F'FO7$F1FO7$FCFO" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "plot(ulam(3),color=red,axes=boxed);" }}{PARA 13 "" 1 "" {INLPLOT " 6'-%'CURVESG6#7S7$\"\"!F(7$$\"\"\"F(F(7$F*F*7$F(F*7$$!\"\"F(F*7$F/F(7$ F/F/7$F(F/7$F*F/7$$\"\"#F(F/7$F6F(7$F6F*7$F6F67$F*F67$F(F67$F/F67$$!\" #F(F67$F?F*7$F?F(7$F?F/7$F?F?7$F/F?7$F(F?7$F*F?7$F6F?7$$\"\"$F(F?7$FJF /7$FJF(7$FJF*7$FJF67$FJFJ7$F6FJ7$F*FJ7$F(FJ7$F/FJ7$F?FJ7$$!\"$F(FJ7$FW F67$FWF*7$FWF(7$FWF/7$FWF?7$FWFW7$F?FW7$F/FW7$F(FW7$F*FW7$F6FW7$FJFW-% 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